Adaptive time diversity and spatial diversity for OFDM

ABSTRACT

An adaptable orthogonal frequency-division multiplexing system (OFDM) that uses a multiple input multiple output (MIMO) to having OFDM signals transmitted either in accordance with time diversity to reducing signal fading or in accordance with spatial diversity to increase the data rate. Sub-carriers are classified for spatial diversity transmission or for time diversity transmission based on the result of a comparison between threshold values and at least one of three criteria. The criteria includes a calculation of a smallest eigen value of a frequency channel response matrix and a smallest element of a diagonal of the matrix and a ratio of the largest and smallest eigen values of the matrix.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application is a continuation application of U.S. patentapplication Ser. No. 09/750,804 to Shiquan Wu et al., filed Dec. 29,2000, and incorporates its subject matter in its entirety herein byreference. U.S. patent application Ser. No. 09/750,804 claims priorityto U.S. Provisional Patent Application No. 60/229,972, filed Sep. 1,2000, the contents of which are also incorporated in their entiretyherein by reference.

Reference is made to co-pending patent application entitled “ChannelsEstimation For Multiple Input—Multiple Output, Orthogonal FrequencyDivision Multiplexing (OFDM) System”, and incorporates its subjectmatter by reference with respect to channels estimation.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to adapting time diversity and spatial diversityfor use in an orthogonal frequency-division multiplexing (OFDM)environment, using a multiple input and multiple output (MIMO)structure.

2. Discussion of Related Art

A multiple input, multiple output (MIMO) structure has multiplecommunication channels that are used between transmitters and receivers.A space time transmitter diversity (STTD) system may be used on a MIMOstructure, but it will not increase the data throughput. Indeed, for ahigh level configuration, the data rate may even reduce. In an STTDsystem, the transmitters deliver the same information content withinconsecutive symbol duration so that time diversity may be exploited. Toefficiently use the multiple transmitters of the MIMO structure,however, the transmission data rate needs to be increased.

The most straightforward solution to increase the transmission data rateis to in forward error correction (FEC) dump independent data to eachtransmitter. A forward error correction (FEC) encoder produces in-phaseand quadrature-phase data streams for the digital QAM modulator inaccordance with a predetermined QAM constellation. The QAM modulator mayperform baseband filtering, digital interpolation and quadratureamplitude modulation. The output of the QAM modulator is a digitalintermediate frequency signal. A digital to analog (D/A) convertertransforms the digital IF signal to analog for transmission.

The problem arises, however, as to how to safely recover the transmitteddata. For a 2×2 system (two transmitters, two receivers) for example,after the channel information is obtained, the recovery process entailsformulating two equations with two unknowns that need to be solved. Thetwo unknowns may be determined only if the 2×2 channel is invertible. Inpractice, however, two situations may be encountered, i.e., the channelmatrix is rank deficient so the unknowns cannot be determined or thefrequency response channel matrix is invertible but has a very smalleigen value.

The first situation arises when the channels are highly correlated,which may be caused either by not enough separation of the transmittersor by homology of the surroundings. For the second situation, althoughthe equations are solvable, the solution can cause a high bit error rate(BER), because a scale up of the noise can result in an incorrectconstellation point.

Orthogonal frequency-domain multiplexing (OFDM) systems were designedconventionally for either time diversity or for space diversity, but notboth. The former will provide a robust system that combats signal fadingbut cannot increase the data rate capacity, while the latter canincrease the data rate capacity but loses the system robustness. An OFDMsignal contains OFDM symbols, which are constituted by a set ofsub-carriers and transmitted for a fixed duration.

The MIMO structure may be used for carrying out time diversity for anOFDM system. For instance, when one transmitter transmits an OFDMsignal, another transmitter will transmit a fully correlated OFDM signalto that transmitted by the one transmitter. The same OFDM signal istransmitted with, for instance, a fixed OFDM duration.

On the other hand, spatial diversity entails transmitting independentsignals from different transmitters. Thus, transmitting two independentOFDM signals from two transmitters, respectively, results in a doubledata rate capacity from the parallel transmission that occurs.

When the signal to noise ratio (SNR) is low, the frame error rate (FER)is large, so that a data packet transmission will be decoded incorrectlyand will need to be retransmitted. The quality of service (QoS) definesthe number of times that the same packet can be retransmitted, e.g.,within an OFDM architecture. The OFDM system on a MIMO structure,therefore, should be adaptable to ensure that the QoS is maintained.

For any given modulation and code rate, the SNR must exceed a certainthreshold to ensure that a data packet will be decoded correctly. Whenthe SNR is less than that certain threshold, the bit error rate (BER) islarger, which results in a larger FER. The larger the FER, the moreretransmissions of the same packet will be required until the packet isdecoded correctly. Thus, steps may need to be taken to provide the OFDMsystem with a higher gain. If the SNR is at or above the threshold, thenthere is no need to increase the gain of the architecture to decode thedata packets correctly. One challenge is to adapt the OFDM system to usetime diversity when signal fading is detected as problematic and to usespatial diversity at other time to increase the data rate transfer.

In a conventional OFDM system, there are many OFDM modes, for examplesare the 1k mode (1024 tones) and the half k mode (512 tones). For 1kmode, the number of sub-carriers is 1024 and for the half k mode, thenumber of sub-carriers is 512. The 1k mode is suitable for a channelwith long delay and slow temporal fading, while the 512 mode is suitablefor the channel with a short delay and fast temporal fading. But whichmode will be used is really depending on the real environment.

A transaction unit of a conventional OFDM signal is an OFDM frame thatlasts 10 ms. Each OFDM frame consists of 8 OFDM slots and each slotlasts 1.25 ms. Each OFDM slot consists of 8 OFDM symbols and some of theOFDM symbols will be the known preambles for access and channelsestimation purposes. An OFDM super frame is made up of 8 OFDM frames andlasts 80 ms.

In addition to transmitted data, an OFDM frame contains a preamble,continual pilot sub-carriers, and transmission parametersub-carriers/scattered sub-carriers. The preamble contains OFDM symbolsthat all used for training to realize timing, frequency and samplingclock synchronization acquisitions, channel estimation and a C/Icalculation for different access points. The continual pilotsub-carriers contain training symbols that are constant for all OFDMsymbols. They are used for tracking the remaining frequency/samplingclock offset after the initial training.

The transmission parameter sub-carriers/scattered sub-carriers arededicated in each OFDM symbol and reserved for signaling of transmissionparameters, which are related to the transmission scheme, such aschannel coding, modulation, guarding interval and power control. Thetransmission parameter sub-carriers are well protected and therefore canbe used as scattered pilot sub-carriers after decoding.

One application for determining whether sub-carriers should be assignedto time diversity or spatial diversity is to conform to statisticalanalysis of traffic demands during particular times of the day, such aspeak and off-peak. The OFDM system may preferably bias toward eithertime diversity or spatial diversity based on such a statisticalanalysis.

BRIEF SUMMARY OF THE INVENTION

One aspect of the invention pertains to employing adaptive STTD andspatial multiplexing (SM) based on comparing the channel condition ofeach sub-carrier with a threshold. When a sub-carrier is accommodated onchannels that have a “well conditioned” channel matrix, spatialmultiplexing may be used to create independent transmission paths andtherefore increase the data rate. A “well conditioned” channel matrixarises when the smallest eigen value is not too small as compared to athreshold value, such as the noise power increase when multiplied by itsinverse. For those sub-carriers whose channel matrices have smallereigen values, the receiver cannot recover the parallel transmittedinformation symbols. As a result, STTD is used to guarantee a robustsystem.

Encoders associated with the transmitter side encode or classifysub-carriers in accordance with one of two groups based on a feedbacksignal; one of the groups is to forward error correction (FEC) timediversity and the other of the two groups is to forward error correction(FEC) spatial diversity. This grouping is based on results from acomparison made at the receiver side between a threshold value andeither a calculated smallest eigen value of a frequency response matrix,the smallest element in a diagonal of the matrix, or a ratio of thelargest and smallest eigen values in the matrix.

The threshold value is based on the transmitter and receiver antennaconfiguration, environmental constraints of the OFDM communicationsystem, and/or on statistical analysis of communication traffic demands.The estimate value is derived from channel estimation of multiplechannels of multi-input multi-output (MIMO) type systems.

Time diversity is used to reduce adverse signal fading. Spatialdiversity is used to increase the data rate, which time diversity cannotdo. When sub-carriers use time diversity, it means that signal fading isstrong so that parallel transmission of data packets can not be done toovercome the insufficient gain problem. Instead, time diversity is usedto get the necessary gain for the OFDM system, even though the data ratecapacity suffers. An SNR gain is assured with time diversity, because ofthe orthogonality matrix pattern inherent among transmitted samples inthe OFDM system. On the other hand, when sub-carriers use spatialdiversity, signal fading is weak so that parallel transmissions mayoccur to increase the data rate capacity. Thus, there is no need toincrease the gain of the OFDM system, which means that the data rate maybe increased.

In operation, the OFDM system of the invention may start transmission ofdata packets with either time diversity or spatial diversity. Thereceiver side will estimate the channels and decode the data packets.After the channel information, is obtained, the receiver side willcalculate the eigen values of the channel matrices to the extentpossible. The controller then determines whether the sub-carrier to usetime diversity or spatial diversity based on one of three criteria (onlyone of which is dependent upon the eigen value calculation). Thereceiver then reports back or feedbacks to the transmitter side withthis information, i.e., about whether the sub-carrier is to use timediversity or spatial diversity so as to trigger the next round oftransmission accordingly.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the present invention, reference is madeto the following description and accompanying drawings, while the scopeof the invention is set forth in the appended claims.

FIG. 1 is a schematic representation of a generic multi-input,multi-output orthogonal frequency-division multiplexing transmitter inaccordance with an embodiment of the invention.

FIG. 2 is a schematic representation of an orthogonal frequency-divisionmultiplexing symbol.

FIG. 3 is a space time transmitter diversity (STTD) orthogonalfrequency-division multiplexing (OFDM) encoder for loading data to asub-carrier in G1 which will be specified in the forthcoming sections.

FIG. 4 is a spatial multiplexing (SM) orthogonal frequency-divisionmultiplexing (OFDM) encoder for loading data to a sub-carrier in G2which will be specified in the forthcoming sections.

FIG. 5 is a schematic representation of two pure STTD transmitters thatsave one half of the IFFT computation.

FIG. 6 is a schematic representation of four pure STTD transmitters thatsave three fourths of the IFFT computation.

FIG. 7 is a schematic representation a generic receiver structure.

FIG. 8 is a schematic representation of configurations of a two receiverantenna case and a three receiver antenna case.

DETAILED DESCRIPTION OF THE INVENTION

The invention concerns a practical time and spatial diversitycombination that fits into an OFDM system. The OFDM system of theinvention can automatically adapt the channel variation and make tradeoff between time diversity and spatial diversity. In an exemplaryenvironment, the data rate can be increased 1.8 times for 2×2configuration (2 transmitters, 2 receivers), which gives 80 Mbps, and2.7 times for 3×3 configuration) 3 transmitters, 3 receivers) whichgives 121 Mbps within 6 MHz, while keep the robustness of the system.

Turning to the drawing, FIG. 1 shows a generic MIMO and OFDM transmittersystem. In the figure, STTD and SM are the abbreviations ofSpace-Time-Transmitter Diversity and Spatial Multiplexing. The MIMO OFDMis configured as two level adaptations as shown in FIG. 1, namely,space/time diversity adaptation and coding/modulation adaptation. Thespace/time diversity adaptation is determined by the carrier tointerference power ratio or signal to noise power ratio.

Information data is fed into adaptive coding modulation; the modulationis multiplexed and fed into adaptive space/time diversity encoding andassignment. A receiver feedback to provide feedback signals to theadaptive coding of modulation, multiplexer and adaptive space/timediversity is also provided. The multiplexed signals in the adaptivespace/time diversity pass through STTD/SM OFDM encoders and the encodedsignals transmit to associated antennas. The adaptive coding andmodulation includes a forward error correction (FEC) encoder, aninterleaver and an m-PSK modular.

If x MHz bandwidth is available, then Orthogonal Frequency DivisionMultiplexing OFDM is to chop this whole spectrum into many small piecesof equal width and each of them will be used as a carrier. The width ofthe piece will be determined by delay spread of the targetedenvironment.

The STTD/OFDM encoder is responsible for the assignment of theconstellation points to each sub-carrier. For M transmitters, M OFDMsymbols data are loaded in general (so the bit loading will becalculated according to this number), but it will depend on the STTDstructure. FIG. 2 illustrates one OFDM symbol.

For each sub-carrier that is indexed k, its loading will be determinedby its corresponding channel condition. For N receivers, the frequencychannel responses may be represented by an M×N matrix, say H(k). Thechannel condition will be described by one of the following 3 criteria.

-   1. Smallest eigen value of H(k)H(k)*-   2. Smallest element of the diagonal of H(k)H(k)*-   3. The ratio of largest and smallest eigen values of H(k)H(k)*

A set of thresholds for each criterion and for each system configurationis used. These thresholds will be service parameters and can be used asquality of service (QoS) or billing purposes.

With each criterion and a given threshold, all the sub-carriers will beclassified into two groups G1 and G2 by a controller at the receiverside. The controller directs the transmission of a feedback signalindicative of the result of the classification. The feedback signal isreceived at the transmitter side and interpreted by a controller at thetransmitter side. The sub-carriers classified in G1 will use STTDencoder at the transmission side while those classified in G2 will usethe SM encoder at the transmission side.

After the sub-carriers have been classified into the two groups G1 andG2, the modulation scheme on each sub-carrier will be determined by theestimated C/I (carrier to interference ratio) or SNR (signal to noiseratio). As a result, a modulation scheme, such as QPSK or m-PSK orvarious QAM, will be selected to satisfy QoS (quality of service) basedon the determination made by the estimated C/I or SNR. This is anotherlevel adaptation that may maximize the throughput gain.

For instance, when the QoS is defined, the FER (frame error rate) may beten percent. The goal is to choose a modulation scheme according to theperceived C/I or SNR to satisfy this QoS, yet still maximizing thethroughput of data flow. To achieve this, a pre-defined look-up tablemay be accessed that is in accordance with various QoS.

In determining which modulation scheme will satisfy the criteria, theC/I or SNR estimation is done during mobile access, after looking forthe strongest signal from the base station first. Based on suchknowledge and estimation, one is able to get a rough idea as to whichmodulation scheme should be used. Regardless of the modulation schemeselected initially, the invention is configured to automatically adapttoward whichever modulation scheme represents the optimal modulation.

FIG. 3 shows how to load data on sub-carrier k for a situation involving2 transmitters for example. This data loading is done within a pair ofOFDM symbols. As can be appreciated, apparently one sample has beentransmitted twice within 2 OFDM symbols duration via 2 transmitters.Thus, the data rate is the same as for the one transmitter OFDM system.

FIG. 4 shows how to load data on sub-carrier k in G2 for a situationinvolving 2 transmitters. In this case, each transmitter transmitsindependent data and therefore the data rate is double for 2transmitters and M times for M transmitters.

The adaptive time diversity and spatial diversity for OFDM works asfollows. Starting out, an STTD mode is used for all sub-carriers. Thereceiver estimates the channel profiles and then directs a feedback ofits preference either to STTD or spatial multiplexing (SM) on eachsub-carrier.

The whole sub-carrier indices {K_(min), K_(min)+1, . . . , K_(max)} arethen divided into two disjoint subsets I_(sttd) and I_(sm). The one withfewer elements will be the feedback to the transmitters. The extremecase is that one of them is an empty set, which means use of either pureSTTD or pure SM. As in the pure STTD system, the transmitters alwaysconsider two OFDM symbols as the basic transmission unit for 2×2configuration and M OFDM symbols for a system has M transmitters.

The number of input bits, however, needs to be calculated according to amodulation scheme and a dynamic distribution of I_(sttd) and I_(sm).More precisely, the number of bits needed for the two consecutive OFDMsymbols is 2×|I_(sttd)|L+4×|I_(sm)|L, where L is the modulation levelwhich equals to 2, 3, 4 5, 6, 7, 8.

When a granularity problem arises, the two OFDM symbols are repacked tofit the granularity by removing some sub-carriers from I_(sm) intoI_(sttd). This may sacrifice the data rate somewhat, but keep the systemrobust.

In the receiver side, a quadrature amplitude modulation QAM de-mappingblock is used to de-map the received data according to I_(sttd) andI_(sm).

STTD is the baseline of the service quality. This means that whenparallel transmission is carried out in the designated communicationchannels, then it is guaranteed parallel transmission, because the BERor FER will be controlled to achieve the necessary QoS. The transmitterswill propagate the transmissions at the same constant power and themodulation will be the same for each transmitter. Thus, no power pouringtechnique needs to be employed.

Three thresholds are used to classify the sub-carriers. Indeed, thethreshold can be used as a service parameter and tuned aggressive toeither STTD mode or SM mode according to customer demand, i.e., based onstatistical analysis of that demand.

As an example, for the case where the smallest eigen value is used asthe threshold in a 2×2 configuration (2 transmitters, 2 receivers),there is a 60% opportunity to do parallel transmission with 0.5 as thethreshold value, which may be scale the noise 3 dB up. For a 2×4configuration (2 transmitters, 4 receivers), there is an 80% opportunityto do parallel transmission with 1 as the threshold value, which mayeven reduce the noise.

FIG. 5 shows a special, but very practical situation, which shows twopure STTD transmitters that save ½ of an inverse fast Fourier transform(IFFT) computation. The present invention may automatically switch tothis scenario in a vulnerable environment involving 2 transmitters.

Conventionally, one would expect each transmitter to transmit 2 OFDMsymbols every 2 OFDM symbol duration. Thus, there are 4 OFDM symbolstransmitted for every 2 OFDM duration that go through a respectiveindependent IFFT computation engine. This means that a complex numberIFFT computation is expected to be conducted four times.

For a pure STTD implementation with 2 and 4 transmit antennas, thecomputational efficient implementation is shown in FIGS. 5 and 6respectively. The scheme in FIG. 5 requires ½ of the IFFT computationand the scheme in FIG. 6 requires ¼ of the IFFT computation as comparedwith a straightforward implementation that performs the computationsseparately.

In accordance with FIG. 5, however, there is data crossing between twotransmitters, which saves two IFFT computations. Yet, it provides fourIFFT outputs, which is exactly the same results where four independentIFFTs are used. Although four IFFT operations are shown in FIG. 5, theyare operating on real vectors, which means the computational complexityof a real IFFT equals the complex IFFT with a half size. Therefore, thecomputational time saving comes from the relationship between IFFT on avector and its conjugate.

In FIG. 5, the bits are coded bits, which are the input to variableM-PSK/QAM mapping. The mapping will map the bits to the correspondingconstellation points according to the Gray rule; constellation pointshere refer to any modulation scheme, such as QPSK, m-PSK, QAM, etc. Theconstellation vector will be inserted with a pilot into a multiplex andthen into first in first out (FIFO) buffers.

The designations S₀, S₁, S₂, S₃, S₂₀₄₆, S₂₀₄₇, in the FIFO bufferrepresent complex vectors. The function Re { } refers to just taking thereal part of the complex vector. The designation Im { } refers to justtaking the imaginary part of the complex vector. The real and imaginaryparts are fed as input into IFFTs. The designation D/A refers to adigital to analog converter.

The transmission order for the first transmitter is OFDM symbol b andthen d . . . ; the transmission order for the second transmitter is OFDMsymbol g and then f etc. Before each OFDM symbol is transmitted, thecyclic extension will be appended somewhere in the OFDM symbol.

Periodically inserted preambles will serve for the timing recovery,framing, frequency offset estimation, clock correction and overallchannel estimation The estimated channel samples will be used for thecontinuous spectrum channel reconstruction. Pilot symbols will serve forphase correction, final tuning of channel estimation.

The mathematical equivalence for FIG. 5 is as follows.${b = {{IFFT}\begin{bmatrix}S_{0} \\S_{2} \\\vdots \\S_{2046}\end{bmatrix}}},{d = {{IFFT}\begin{bmatrix}{- S_{1}^{*}} \\{- S_{3}^{*}} \\\vdots \\{- S_{2047}^{*}}\end{bmatrix}}},{f = {{IFFT}\begin{bmatrix}S_{1} \\S_{3} \\\vdots \\S_{2047}\end{bmatrix}}},{g = {{IFFT}\begin{bmatrix}S_{0}^{*} \\S_{2}^{*} \\\vdots \\S_{2046}^{*}\end{bmatrix}}}$

FIG. 6 shows four Pure STTD Transmitters that represents a rate ¾ STTDencoder as: T × 1 S(0) −S(1)* S(2)*/sqrt(2) S(2)/sqrt(2) T × 2 S(1)S(0)* S(2)*/sqrt(2) −S(2)/sqrt(2) T × 3 S(2)/sqrt(2) S(2)/sqrt(2)−Re{S(0)} + jIm{S(1)} −Re{S(1)} + jIm{S(0)} T × 4 S(2)/sqrt(2)S(2)/sqrt(2) Re{S(1)} + jIm{S(0)} −Re{S(0)} − jIm{S(1)} Time [0 T] [T2T] [2T 3T] [3T 4T]

Such an STTD encoder encodes every 3 OFDM symbols into 4 OFDM symbolsand transmits to 4 antennas. FIG. 6 scheme requires ¼ IFFT computationcompared to the straightforward implementation. The reason whycomputation is saved is for the same reasons as in FIG. 5. Theparameters there are defined respectively as follows:${b = {{IFFT}\begin{bmatrix}S_{0} \\S_{3} \\\vdots \\S_{3069}\end{bmatrix}}},{g = {{IFFT}\begin{bmatrix}S_{0}^{*} \\S_{3}^{*} \\\vdots \\S_{3069}^{*}\end{bmatrix}}}$ ${f = {{IFFT}\begin{bmatrix}S_{1} \\S_{4} \\\vdots \\S_{3070}\end{bmatrix}}},{d = {{IFFT}\begin{bmatrix}S_{1}^{*} \\S_{4}^{*} \\\vdots \\S_{3070}^{*}\end{bmatrix}}}$ ${q = {{IFFT}\begin{bmatrix}S_{2} \\S_{5} \\\vdots \\S_{3071}\end{bmatrix}}},{u = {{IFFT}\begin{bmatrix}S_{2}^{*} \\S_{5}^{*} \\\vdots \\S_{3071}^{*}\end{bmatrix}}}$

FIG. 7 is an abstract diagram of a generic receiver structure. STTD/SMOFDM decoder is sub-carrier based decoder. The structure andconfiguration of the STTD/SM OFDM decoder will depend on thearchitecture configuration.

Suppose sub-carrier m is STTD coded, i.e. m belongs to G1. For a 2×2configuration:

S(2m) and S(2m+1) are decoded by solving the following equations$\begin{matrix}{\begin{bmatrix}{y_{1}\left( {q,m} \right)} \\{y_{1}\left( {{q + 1},m} \right)}^{*}\end{bmatrix} = {{\begin{bmatrix}{h_{11}\left( {q,m} \right)} & {h_{21}\left( {q,m} \right)} \\{h_{21}\left( {q,m} \right)}^{*} & {- {h_{11}\left( {q,m} \right)}^{*}}\end{bmatrix}\begin{bmatrix}{s\left( {2\quad m} \right)} \\{s\left( {{2\quad m} + 1} \right)}\end{bmatrix}} +}} \\{\begin{bmatrix}{n_{1}\left( {q,m} \right)} \\{n_{1}\left( {{q + 1},m} \right)}\end{bmatrix}}\end{matrix}$

The assumption here is that the even indexed sample S(2m) is transmittedin qth OFDM and the odd indexed sample S(2m+1) is transmitted in (q+1)thOFDM symbol.

There are 4 equations and two unknowns. So a least mean square solutioncan be obtained by multiplying the coefficient matrix to the receiveddata vector. With the above two pairs, we will get two estimated of thesame pair of samples. Their average will be the output of the decoder.

More statistics are performed after regrouping the equations. In fact,every pair of the equations will result a solution, every 3 equationsalso provide a new estimation, and all the equations will give asolution too. There are 10 combinations in total and therefore 10estimation with these 4 equations. Their average or partial average willbe used as the solution.

A 2×3 configuration is similar to 2×2, involving 6 equations:$\begin{matrix}{\begin{bmatrix}{y_{1}\left( {q,m} \right)} \\{y_{1}\left( {{q + 1},m} \right)}^{*}\end{bmatrix} = {{\begin{bmatrix}{h_{11}\left( {q,m} \right)} & {h_{21}\left( {q,m} \right)} \\{h_{21}\left( {q,m} \right)}^{*} & {- {h_{11}\left( {q,m} \right)}^{*}}\end{bmatrix}\begin{bmatrix}{s\left( {2\quad m} \right)} \\{s\left( {{2\quad m} + 1} \right)}\end{bmatrix}} +}} \\{\begin{bmatrix}{n_{1}\left( {q,m} \right)} \\{n_{1}\left( {{q + 1},m} \right)}\end{bmatrix}}\end{matrix}$ $\begin{matrix}{\begin{bmatrix}{y_{2}\left( {q,m} \right)} \\{y_{2}\left( {{q + 1},m} \right)}^{*}\end{bmatrix} = {{\begin{bmatrix}{h_{12}\left( {q,m} \right)} & {h_{22}\left( {q,m} \right)} \\{h_{22}\left( {q,m} \right)}^{*} & {- {h_{12}\left( {q,m} \right)}^{*}}\end{bmatrix}\begin{bmatrix}{s\left( {2\quad m} \right)} \\{s\left( {{2\quad m} + 1} \right)}\end{bmatrix}} +}} \\{\begin{bmatrix}{n_{2}\left( {q,m} \right)} \\{n_{2}\left( {{q + 1},m} \right)}\end{bmatrix}}\end{matrix}$ $\begin{matrix}{\begin{bmatrix}{y_{3}\left( {q,m} \right)} \\{y_{3}\left( {{q\quad + \quad 1},m} \right)}^{*}\end{bmatrix} = {{\begin{bmatrix}{h_{13}\left( {q,m} \right)} & {h_{23}\left( {q,m} \right)} \\{h_{23}\left( {q,m} \right)}^{*} & {- {h_{13}\left( {q,m} \right)}^{*}}\end{bmatrix}\begin{bmatrix}{s\left( {2\quad m} \right)} \\{s\left( {{2\quad m} + 1} \right)}\end{bmatrix}} +}} \\{\begin{bmatrix}{n_{3}\left( {q,m} \right)} \\{n_{3}\left( {{q + 1},m} \right)}\end{bmatrix}}\end{matrix}$

For a 2×4 configuration, there are 8 equations: $\begin{matrix}{\begin{bmatrix}{y_{1}\left( {q,m} \right)} \\{y_{1}\left( {{q + 1},m} \right)}^{*}\end{bmatrix} = {{\begin{bmatrix}{h_{11}\left( {q,m} \right)} & {\quad{h_{\quad 21}\left( {q,m} \right)}} \\{h_{21}\left( {q,m} \right)}^{*} & {- {h_{11}\left( {q,m} \right)}^{*}}\end{bmatrix}\begin{bmatrix}{s\left( {2\quad m} \right)} \\{s\left( {{2\quad m} + 1} \right)}\end{bmatrix}} +}} \\{\begin{bmatrix}{n_{1}\left( {q,m} \right)} \\{n_{1}\left( {{q + 1},m} \right)}\end{bmatrix}}\end{matrix}$ $\begin{matrix}{\begin{bmatrix}{y_{2}\left( {q,m} \right)} \\{y_{2}\left( {{q + 1},m} \right)}^{*}\end{bmatrix} = {{\begin{bmatrix}{h_{12}\left( {q,m} \right)} & {h_{22}\left( {q,m} \right)} \\{h_{22}\left( {q,m} \right)}^{*} & {- {h_{12}\left( {q,m} \right)}^{*}}\end{bmatrix}\begin{bmatrix}{s\left( {2\quad m} \right)} \\{s\left( {{2\quad m} + 1} \right)}\end{bmatrix}} +}} \\{\begin{bmatrix}{z_{2}\left( {q,m} \right)} \\{z_{2}\left( {{q + 1},m} \right)}\end{bmatrix}}\end{matrix}$ $\begin{matrix}{\begin{bmatrix}{y_{3}\left( {q,m} \right)} \\{y_{3}\left( {{q + 1},m} \right)}^{*}\end{bmatrix} = {{\begin{bmatrix}{h_{13}\left( {q,m} \right)} & {h_{23}\left( {q,m} \right)} \\{h_{23}\left( {q,m} \right)}^{*} & {- {h_{13}\left( {q,m} \right)}^{*}}\end{bmatrix}\begin{bmatrix}{s\left( {2\quad m} \right)} \\{s\left( {{2\quad m} + 1} \right)}\end{bmatrix}} +}} \\{\begin{bmatrix}{n_{3}\left( {q,m} \right)} \\{n_{3}\left( {{q + 1},m} \right)}\end{bmatrix}}\end{matrix}$ $\begin{matrix}{\begin{bmatrix}{y_{4}\left( {q,m} \right)} \\{y_{4}\left( {{q + 1},m} \right)}^{*}\end{bmatrix} = {{\begin{bmatrix}{h_{14}\left( {q,m} \right)} & {h_{24}\left( {q,m} \right)} \\{h_{24}\left( {q,m} \right)}^{*} & {- {h_{14}\left( {q,m} \right)}^{*}}\end{bmatrix}\begin{bmatrix}{s\left( {2\quad m} \right)} \\{s\left( {{2\quad m} + 1} \right)}\end{bmatrix}} +}} \\{\begin{bmatrix}{n_{4}\left( {q,m} \right)} \\{n_{4}\left( {{q + 1},m} \right)}\end{bmatrix}}\end{matrix}$

For a 4×2 configuration, there are 8 equations and 3 unknowns$\begin{matrix}{\begin{bmatrix}{y_{1}\left( {q,m} \right)} \\{y_{1}\left( {{q + 1},m} \right)} \\{y_{1}\left( {{q + 2},m} \right)} \\{y_{1}\left( {{q + 3},m} \right)}\end{bmatrix} = {{\begin{bmatrix}\left. {s\left( {{3\quad m} - 3} \right)} \right) & {s\left( {{3\quad m} - 2} \right)} & \frac{s\left( {{3\quad m} - 1} \right)}{\quad\sqrt{2}} & \frac{s\left( {{3\quad m}\quad - 1} \right)}{\sqrt{2}} \\{- {s\left( {{3\quad m} - 2} \right)}^{*}} & {s\left( {{3\quad m} - 3} \right)}^{*} & \frac{s\left( {{3\quad m} - 1} \right)}{\sqrt{2}} & {- \frac{s\left( {{3\quad m}\quad - 1} \right)}{\sqrt{2}}} \\\frac{{s\left( {{3\quad m} - 1} \right)}^{*}}{\sqrt{2}} & {\quad\frac{\quad{s\left( {{3\quad m} - 1} \right)}^{*}}{\sqrt{2}}} & {\eta\quad(m)} & {\kappa\quad(m)} \\\frac{{s\left( {{3\quad m} - 1} \right)}^{*}}{\sqrt{2}} & {- \frac{{s\left( {{3\quad m}\quad - 1} \right)}^{*}}{\sqrt{2}}} & {\nu\quad(m)} & {\zeta\quad(m)}\end{bmatrix}\begin{bmatrix}{h_{11}\quad(m)} \\{h_{21}\quad(m)} \\{h_{31}\quad(m)} \\{h_{41}(m)}\end{bmatrix}} +}} \\{\begin{bmatrix}n_{11} \\n_{21} \\n_{31} \\n_{41}\end{bmatrix}}\end{matrix}$  η(m)=−Re(s(3(m−1)))+j Im(s(3(m−1)+1)),κ(m)=−Re(s(3(m−1)+1))+j Im ag(s(3(m−1))),ν(m)=Re(s(3(m−1)+1))+j Im(s(3(m−1))), ζ(m)=−Re(s(3(m−1)))−j Imag(s(3(m−1)+1)),h_(k1)(m) is the frequency channel response of the channel betweentransmitter k and receiver 1.

Similarly, the received data for the 4×2 configuration is$\begin{matrix}{\begin{bmatrix}{y_{2}\left( {q,m} \right)} \\{y_{2}\left( {{q + 1},m} \right)} \\{y_{2}\left( {{q + 2},m} \right)} \\{y_{2}\left( {{q + 3},m} \right)}\end{bmatrix} = {{\begin{bmatrix}\left. {s\left( {{3\quad m} - 3} \right)} \right) & {s\left( {{3\quad m} - 2} \right)} & \frac{s\left( {{3\quad m} + 1} \right)}{\sqrt{2}} & \frac{s\left( {{3\quad m} - 1} \right)}{\sqrt{2}} \\{- {s\left( {{3\quad m} - 2} \right)}^{*}} & {s\left( {{3\quad m} - 3} \right)}^{*} & \frac{s\left( {{3\quad m} - 1} \right)}{\sqrt{2}} & {- \frac{s\left( {{3\quad m} - 1} \right)}{\sqrt{2}}} \\\frac{{s\left( {{3\quad m} - 1} \right)}^{*}}{\sqrt{2}} & \frac{{s\left( {{3\quad m} - 1} \right)}^{*}}{\sqrt{2}} & {\eta(m)} & {\kappa(m)} \\\frac{{s\left( {{3\quad m} - 1} \right)}^{*}}{\sqrt{2}} & {- \frac{{s\left( {{3\quad m} - 1} \right)}^{*}}{\sqrt{2}}} & {\nu(m)} & {\zeta(m)}\end{bmatrix}\begin{bmatrix}{h_{12}(m)} \\{h_{22}(m)} \\{h_{32}(m)} \\{h_{42}(m)}\end{bmatrix}} +}} \\{\begin{bmatrix}n_{11} \\n_{21} \\n_{31} \\n_{41}\end{bmatrix}}\end{matrix}$

The solution will be the least mean square solution by enumerating allpossibilities.

Suppose instead that sub-carrier m is SM Coded, i.e. m belongs to G2.For a 2×2 configuration, there are 4 equations and 4 unknowns:$\begin{bmatrix}{\quad{y_{1}\left( {q,m} \right)}} \\{\quad{y_{2}\left( {q,m} \right)}}\end{bmatrix} = {{\begin{bmatrix}{\quad{h_{11}\left( {q,m} \right)}} & {h_{21}\left( {q,m} \right)} \\{\quad{h_{12}\left( {q,m} \right)}} & {h_{22}\left( {q,m} \right)}\end{bmatrix}\begin{bmatrix}{s\left( {2\quad m} \right)} \\{s\left( {{2\quad m} + 1} \right)}\end{bmatrix}} + \begin{bmatrix}{n_{1}\left( {q\quad,m} \right)} \\{n_{1}\left( {q,m} \right)}\end{bmatrix}}$ $\begin{matrix}{\begin{bmatrix}{y_{1}\left( {{q + 1},m} \right)} \\{{y_{2}}_{\quad}\left( {{q + 1},m} \right)}^{*}\end{bmatrix} = {{\begin{bmatrix}{h_{11}\left( {q,m} \right)} & {h_{21}\left( {q,m} \right)} \\{h_{12}\left( {q,m} \right)} & {h_{22}\left( {q,m} \right)}\end{bmatrix}\begin{bmatrix}{s\left( {{2\quad m} + 2} \right)} \\{s\left( {{2\quad m} + 3} \right)}\end{bmatrix}} +}} \\{\begin{bmatrix}{n_{2}\left( {{q + 1},m} \right)} \\{n_{2}\left( {{q + 1},m} \right)}\end{bmatrix}}\end{matrix}$

So the 4 unknowns can be estimated by the least mean square solutions.For a 2×3 configuration, there are 6 equations and 4 unknowns.$\begin{bmatrix}{y_{1}\left( {q,m} \right)} \\{y_{2}\left( {q,m} \right)} \\{y_{3}\left( {q,m} \right)}\end{bmatrix} = {{\begin{bmatrix}{h_{11}\left( {q,m} \right)} & {h_{21}\left( {q,m} \right)} \\{h_{12}\left( {q,m} \right)} & {h_{22}\left( {q,m} \right)} \\{h_{13}\left( {q,m} \right)} & {h_{23}\left( {q,m} \right)}\end{bmatrix}\begin{bmatrix}{s\left( {2\quad m} \right)} \\{s\left( {{2\quad m} + 1} \right)}\end{bmatrix}} + \begin{bmatrix}{n_{1}\left( {q,m} \right)} \\{n_{2}\left( {q,m} \right)} \\{n_{3}\left( {q,m} \right)}\end{bmatrix}}$ $\begin{matrix}{\begin{bmatrix}{y_{1}\left( {{q + 1},m} \right)} \\{y_{2}\left( {{q + 1},m} \right)} \\{y_{3}\left( {{q + 1},m} \right)}\end{bmatrix} = {{\begin{bmatrix}{h_{11}\left( {{q + 1},m} \right)} & {\quad{h_{21}\left( {{q + 1},m} \right)}} \\{h_{12}\left( {{q + 1},m} \right)} & {\quad{h_{22}\left( {{q\quad + 1},m} \right)}} \\{h_{13}\left( {{q + 1},m} \right)} & {\quad{h_{23}\left( {{q + 1},m} \right)}}\end{bmatrix}\begin{bmatrix}{s\left( {{2\quad m} + 2} \right)} \\{s\left( {{2\quad m} + 3} \right)}\end{bmatrix}} +}} \\{\begin{bmatrix}{n_{1}\left( {{q + 1},m} \right)} \\{n_{2}\left( {{q + 1},m} \right)} \\{n_{3}\left( {{q + 1},m} \right)}\end{bmatrix}}\end{matrix}$

For a 2×4 configuration, there are 8 equations and 4 unknowns. For a 3×3configuration, there are 9 equations and 9 unknowns.

In accordance with the inventive architecture, the data rate can be ashigh as 70 Mbps for 2×2 and 120 Mbps for 3×3 within 6 MHz spectrum.

An exemplary optimal threshold value for a 2×2 configuration is 0.5. Anexemplary optimal threshold value for a 2×4 configuration is 1.0. Anexemplary optimal threshold value for a 3×3 configuration is 1.2. Anexemplary optimal threshold value for a 2×3 configuration is 1.0. Byexemplary optimal threshold value, the intent is to attain a value thathas a trade-off between time and spatial diversity that yields both arelatively high robustness and relatively high data packet ratetransfer.

As can be appreciated for each of the afore-mentioned configurations,there are a certain number of equations and a certain number ofunknowns. In an over-determined system, the number of equations isgreater than the number of unknowns. Thus, for a 2×2 configuration,there are two unknowns but four equations may be formulated. If there isno noise, any two of them (six pairs), or any three of them (fourtriples) or all of the four equations (one quadratic) will give the sameanswer. The difference is when noise is present, because thecombinations with then give different solutions. Since some of thesolutions may be good while others are bad, different combinations arechosen, but those combinations that result in large derivations are tobe avoided. The idea is to use a sub-set of the over determined linearequations to estimate the solution and then average all the possiblesolutions that seem viable. The averaging may be done with a least meansquare solution, which is a conventional mathematical technique.

FIG. 8 compares a two receiver antenna case and a three receiver antennacase. With respect to the three receiver antenna case, the number ofreceiver antennas is greater than the number of transmitter antennas. Asa consequence, the receiver has additional redundancy, the receiver hasvarious configurations, and the configurations yield several differentdecoding results. The most reliable solution can be selected from amongthem or all the solutions may be averaged to obtain a final result.

While the foregoing description and drawings represent the preferredembodiments of the present invention, it will be understood that variouschanges and modifications may be made without departing from the spiritand scope of the present invention.

1. An apparatus for transmitting data, comprising: an orthogonal frequency division multiplexing (OFDM) encoder for loading: a first data on a sub-carrier of an OFDM symbol associated with an antenna; a second data on a sub-carrier of an another OFDM symbol associated with the antenna; said first and said second data on sub-carriers of OFDM symbols associated with an another antenna according to at least one mapping rule, wherein said at least one mapping rule is a conjugate mapping rule; said antenna transmits said first data; said antenna transmits said second data; and said another antenna transmits said first and said second data; wherein said transmission of said first data with said another antenna is transmitted subsequent to said transmission of said first data with said antenna; and said transmission of said second data with said antenna is transmitted subsequent to said transmission of said second data with said another antenna.
 2. The apparatus of claim 1, wherein said OFDM encoder is configured to load: said first data on said sub-carrier of said OFDM symbols associated with said another antenna according to said conjugate mapping rule; and said second data on said sub-carrier of said OFDM symbol associated with said another antenna according to a negative conjugate mapping rule.
 3. The apparatus of claim 2, wherein a rate of transmission of said first data with said antenna is substantially equal to a rate of transmission of said first data with said another antenna; and a rate of transmission of said second data with said antenna is substantially equal to a rate of transmission of said second data with said another antenna.
 4. An apparatus for transmitting data, comprising: an orthogonal frequency division multiplexing (OFDM) encoder configured to load: a first data on a sub-carrier of an OFDM symbol associated with an antenna; a second data on a sub-carrier of an another OFDM symbol associated with the antenna; and said first and said second data on sub-carriers of OFDM symbols associated with another antenna according to a first conjugate mapping rule and a second conjugate mapping rule, to thereby produce a first mapped data and a second mapped data; wherein said antenna is configured to transmit said first data; said antenna is configured to transmit said second data; said another antenna is configured to transmit said first mapped data; said another antenna is configured to transmit said second mapped data; and respective transmissions with said another antenna are subsequent to corresponding transmissions with said antenna.
 5. The apparatus of claim 4, wherein said second conjugate mapping rule is a negative conjugate mapping rule.
 6. The apparatus of claim 5, wherein a rate of transmission of said first data with said antenna is substantially equal to a rate of transmission of said first mapped data with said another antenna; and a rate of transmission of said second data with said antenna is substantially equal to a rate of transmission of said second mapped data with said another antenna.
 7. The apparatus of claim 4, wherein said first and second conjugate mapping rules are the same. 